"We identified and isolated all guests and crew who had close contact with this guest, and each of those individuals have subsequently tested negative for the virus," said the company in a statement.
"That we were able to quickly identify this single case and take immediate action is a sign that the system is working as it was designed to do," it said.
The company which unveiled a new health pledge for the sailings promised a range of Covid precautions, including continued daily temperature checks and rapid covid tests as part of medical evaluations.
Local media has reported that an additional Royal Caribbean cruise departure scheduled to depart on Thursday, will go ahead as planned.
On 3 December the cruise company celebrated the partnership with the Singaporean government in trialling the 'pilot cruises', with a pledge from managing director Angie Stephen pledging a "commitment to providing our guests with the safest possible cruise experience."